Related papers: Adaptive Learning Rates for Support Vector Machine…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…
Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot…
Self-supervised learning attempts to learn representations from un-labeled data; it does so via a loss function that encourages the embedding of a point to be close to that of its augmentations. This simple idea performs remarkably well,…
The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…
This paper proposes a frequent pattern data mining algorithm based on support vector machine (SVM), aiming to solve the performance bottleneck of traditional frequent pattern mining algorithms in high-dimensional and sparse data…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…
Support Vector Machine (SVM) has been one of the most successful machine learning techniques for binary classification problems. The key idea is to maximize the margin from the data to the hyperplane subject to correct classification on…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We develop Gaussian approximations for high-dimensional vectors formed by second-order $U$- and $V$-statistics whose kernels depend on sample size under independent but not identically distributed (i.n.i.d.) sampling. Our results hold…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
Recent work has shown that Transformers can perform in-context learning for linear regression under restrictive assumptions, including i.i.d. data, Gaussian noise, and Gaussian regression coefficients. However, real-world data often violate…
Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification. They can be implemented in either their primal or dual form. The latter requires solving a linear system,…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…